Competition between Pairing and Ferromagnetic Instabilities in Ultracold Fermi Gases near Feshbach Resonances

Abstract

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.Ferromagnetism in itinerant Fermions is a prime example of a strongly interacting system. Most theoretical treatments rely on a mean-field Stoner criterion [1], but whether this argument applies beyond mean-field remains an open problem. It is known that the existence of the Stoner instability is very sensitive to the details of band structure and interactions [2][3][4], however how to account for these details in realistic systems remains poorly understood. Exploring the Stoner instability with ultracold atoms has recently attracted considerable attention. Following theoretical proposals [5], the MIT group made use of the tunability [6] and slow time scales [7-10] of ultracold atom systems to study the Stoner instability [11]. Signatures compatible with ferromagnetism, as understood from mean-field theory [12], were observed in experiments: a maximum in cloud size, a minimum in kinetic energy and a maximum in atomic losses at the transition. However, no magnetic domains were resolved.An important aspect of the MIT experiments is that they were done dynamically: the Fermi gas was originally prepared with weak interactions and then the interactions were ramped to the strongly (repulsive) regime. Dynamic rather than adiabatic preparation was used in order to avoid production of molecules. This raises the question of what are the dominant instabilities of the Fermi gas in the vicinity of a Feshbach resonance.Naively, one would expect that on the BEC-side, molecule production is slow, as it requires a three-body process. Therefore, instability towards Stoner ferromagnetism would dominate over the instability toward molecule production. In this picture, one would expect that quenches to the attractive (BCS) regime always yield an instability towards pairing, whereas quenches to the repulsive (BEC) regime an instability towards ferromagnetism for sufficiently strong interactions.In this Letter, we argue that this picture, which was used to interpret the MIT experiments, is incomplete. Near the Feshbach resonance, even on the BEC side, pair production remains a fast two-body process as long as the Fermi sea can absorb the molecular binding energy. As a result, near the Feshbach resonance, both on the BEC and the BCS side, the pairing and the Stoner instabilities compete directly. We now

Tan relations in one dimension

“…In practice, for ultracold gases, the repulsive branch at positive scattering lengths is only metastable. Therefore, a calculation of the energy on this branch alone is not sufficient to determine the conditions for ferromagnetism at least as a metastable state [44]. For example, a variational calculation of the energy of a single flipped spin in the background of a fully polarized up-spin Fermi sea with wave vector k F ↑ indicates that the fully polarized state is stable if k F ↑ a > 2.35 [20].…”

“…In the experiment [19], the gas is initially prepared in the weakly interacting limit k F a ≪ 1 and then the interactions are quickly ramped to the strongly repulsive regime k F a ≫ 1 in order to avoid production of bound dimers [43]. An analysis of the dynamic competition between a putative formation of ferromagnetic domains within an RPA-approximation and the formation of pairs indicates that the growth rate of the latter instability is always faster [44]. In particular, as shown by these authors, anomalies of the kind seen experimentally can be explained in terms of pair formation rather than incipient ferromagnetism (see also [45]).…”

Quasi-one-dimensional atomic gases across wide and narrow confinement-induced resonances

“…as to why the repulsive Fermi gas in a 3D homogenous system is unstable close to Feshbach resonance [29][30][31]. For instance, the instability has been attributed to the shifted resonance in the background of a Fermi sea [29], the pairing instability dominating over ferromagnetism instability [30], or the vanishing zero-momentum molecule due to Pauli-blocking effect of Fermi-sea atoms [31].…”

“…For instance, the instability has been attributed to the shifted resonance in the background of a Fermi sea [29], the pairing instability dominating over ferromagnetism instability [30], or the vanishing zero-momentum molecule due to Pauli-blocking effect of Fermi-sea atoms [31]. All these studies can lead to the same conclusion at low temperatures, i.e., the 3D Fermi gas becomes unstable at the place where a s is comparable to the inter-particle distance (1/k F ), or equivalently, the two-body binding energy (E b ∼ 1/ma 2 s ) is comparable to the Fermi energy (E F ∼ k 2 F /m).…”

Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture

“…Our spectroscopic approach has confirmed the existence of the predicted repulsive branch [9,12,13] and has demonstrated that the repulsive polaron can exist as a well-defined quasiparticle even deep in the strongly interacting regime. The long lifetime of the repulsive polaron in our system, which we ascribe to the finite effective range of the interparticle interaction, may be a key factor to overcome the problem of decay into molecular excitations [11,19] in the experimental investigation of metastable many-body states that rely on repulsive interactions. In particular, the creation of states with two fermionic components phase-separating on microscopic or macroscopic scales [5][6][7][8]10, 11] appears to be an intriguing near-future prospect.…”